This invention relates generally to the field of geophysical prospecting. More particularly, the invention relates to an automated two-dimensional inversion method for true resistivity of reservoir formations from a dual laterolog (DLL) tool""s borehole measurements.
The accuracy of hydrocarbon saturation calculated from well logs, an essential component of petrophysical resource assessment, is fundamentally dependent upon accurate determination of the true formation resistivity (Rt). Apparent formation resistivity (Ra), as measured by a logging tool, however, is not equal to true formation resistivity (Rt) in most logging environments because of the limitations of tool physics and non-ideal borehole conditions. It is known in the art that deep-reading resistivity tools cannot resolve formations less than a few feet thick, and cannot make accurate true resistivity (Rt) measurements when the borehole diameter is variable (rugosity), and when the borehole fluid with a different resistivity than formation fluids has seeped into the formation (invasion), thereby altering the resistivity of the invaded zone (Rxo).
The traditional method of correcting these environmental effects on resistivity logs has been to use chartbooks provided by logging service companies. However, chartbooks only contain a limited number of charts with strict assumptions (e.g., borehole diameter, mud resistivity, and 2 Rt/Rxo ratio) that a chart can seldom match real world examples. Therefore, chartbook corrections may only serve to make a qualitative estimation. Furthermore, the nonlinear resistivity tool response (due to borehole diameter, mud resistivity, invasion, and bed thickness or shoulder bed effects all together) can not be corrected from the chartbooks"" corrections without assumptions of linear superposition.
Computer inverse modeling of resistivity tool response can be conducted to convert apparent resistivity from logs into a response profile that may closely approximate reality. In fact, modem environmental correction charts provided by service companies are the result of computer forward modeling. In general, the inverse modeling involves replicating the observed field log by numerically solving the mathematical boundary value problems of the electrical or electromagnetic fields generated by a specific resistivity tool under a predefined layered-earth model. To the degree that the field log and the computed tool response are in acceptable agreement through iterative forward modeling, the underlying earth model may be considered as one possible representation of the formation""s true resistivity profile. Mathematically, such an inversion process attempts to fit the computed tool response under a set of earth parameters (e.g., bed thickness, Rt, Rm, Rxo, borehole diameter and invasion depth) to an actual field resistivity log, or a set of actual field logs. The parameters in the earth model can be refined by solving least-squares problems through the iterative process to minimize the sum of the squares of the errors between the computed tool response and the measured field log. The iteration may continue until the fit between the computed and field logs reaches predetermined criteria.
With the advent of modeling codes and the significant increase in computing power, resistivity tool response modeling has become a feasible option for formation evaluation. Strict 2D inversion of resistivity logging tool measurements based on iterative 2D forward modeling with finite element or hybrid methods are described in Gianzero, S., Lin, Y., and Su, S., 1985, xe2x80x9cA new high speed hybrid technique for simulation and inversion of resistivity logsxe2x80x9d, SPE 14189; Liu, Q., H., 1994, xe2x80x9cNonlinear inversion of electrode-type resistivity measurementsxe2x80x9d, IEEE on Geoscience and Remote Sensing, Vol. 32, No. 3, pp 499-507; and Mezzatesta, A. G., Eckard, M. H., Strack, K. M., 1995, xe2x80x9cIntegrated 2D Interpretation of Resistivity Logging Measurements by Inversion Methodsxe2x80x9d, Paper-E, SPWLA 36th Annual Logging Symposium Transactions. However, these methods are very computer time consuming. The massive computation required by some of the above methods may only be performed on super computers, making its application to well logging interpretation impractical.
Thus, the need exists for a computationally efficient method for 2D inversion of resistivity from dual laterolog measurements.
The present invention is a method for 2D inversion of true resistivity from dual laterolog tool measurements, using a pre-calculated look-up table. First, an initial earth model is derived and divided into intervals. A 2D tool response is calculated in each interval using the earth model. Matching is checked between the calculated 2D tool response and the tool measurements. The following steps are iterated until the match is satisfactory. A 1D radial tool response is derived in each interval using the pre-calculated look-up table. Shoulder bed effects are approximated in each interval by subtracting the 1D radial tool response from the 2D tool response. A non-linear least square optimization is applied at boundaries of the intervals and local maximum and minimum values in the intervals to update the earth model.